Let G be a graph of degree n with degree sequence $d_1 ≥ d_2 ≥ d_3 ≥ ⋯d_n$. Show that the chromatic number satisfies:
$$χ(G) ≤ 1 + max_i(min(d_i , i − 1))$$
Hint: Assign colors to vertices in order of non-increasing degrees such that no conflict arises. This will produce a valid coloring.
Any ideas on how to prove this question? I don't exactly understand what the formula is saying.